T L  C S C

In this paper, we study the game-theoretic and computational repercussions of Henkin’s partially ordered quantifiers [19]. After defining a gametheoretic semantics for these objects, we observe that tuning the parameter of absentmindedness gives rise to quantifier prefixes studied in [28]. In the interest of computation, we characterize the complexity class PNP q in terms of partially ordered quantifiers, by means of a proof different from Gottlob’s [17]. We conclude with some research questions at the interface of logic, game theory, and complexity theory. We gratefully acknowledge Johan van Benthem, Peter van Emde Boas, Yuri Gurevich, Marcin Mostowski, Eric Pacuit, Gabriel Sandu, Tero Tulenheimo, and the anonymous reviewer. This paper was finalized at Stanford University, whom we thank for hosting us as a visiting scholar.